Finite Group Databasebeta

← #31818239

Subgroups — #31818239

Order 17792.

408 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22581643C211yesmaximal, characteristic, complemented
2#22581307C211yesmaximal, characteristic, complemented
3#22581281C211yesmaximal, characteristic, complemented
4#22581274C211yesmaximal, characteristic, complemented
5#22581253C211yesmaximal, characteristic, complemented
6#22581192C211yesmaximal, characteristic, complemented
7#22581180C211yesmaximal, characteristic, complemented
8#22581172C211yesmaximal, characteristic, complemented
9#22581115C211yesmaximal, characteristic, complemented
10#22581104C211yesmaximal, characteristic, complemented
11C4×#14555773C211yesmaximal, characteristic, complemented
12D4×C139⋊C8C211yesmaximal, characteristic, complemented
13#22580949C211yesmaximal, characteristic, complemented
14C2×#17984763C211yesmaximal, characteristic, complemented
15#546×C139C211yesmaximal, characteristic
16C2×#14555775C2211yescharacteristic, complemented
17C2×#14555773C2211yescharacteristic
18C2×#14555773C2211yescharacteristic
19C22×C139⋊C8C2211yescharacteristic
20C22×C139⋊C8C2211yescharacteristic, complemented
21#17984835—21no—
22#17984834C2211yescharacteristic, complemented
23#17984832—21no—
24#17984823—21no—
25#17984821C2211yescharacteristic
26#17984821C2211yescharacteristic, complemented
27C4×Dic278C2211yescharacteristic, complemented
28#17984801C2211yescharacteristic, complemented
29#17984798—21no—
30C2×C4⋊Dic139C2211yescharacteristic
31#17984775C2211yescharacteristic, complemented
32#17984773C2211yescharacteristic, complemented
33#17984773C2211yescharacteristic, complemented
34C4⋊(C139⋊C8)C2211yescharacteristic, complemented
35#17984766C2211yescharacteristic, complemented
36#17984766C2211yescharacteristic, complemented
37#17984766C2211yescharacteristic, complemented
38#17984765C2211yescharacteristic, complemented
39#17984763C2211yescharacteristic
40#17984763C2211yescharacteristic
41#17984763C2211yescharacteristic
42#17984763C2211yescharacteristic
43#17984763C2211yescharacteristic
44#17984763C2211yescharacteristic
45C22⋊(C139⋊C8)C2211yescharacteristic
46C22⋊(C139⋊C8)C2211yescharacteristic, complemented
47C4×C139⋊C8C2211yescharacteristic, complemented
48C2×#41×C139C2211yescharacteristic
49C22×D4×C139C2211yescharacteristic
50#124×C139C2211yescharacteristic
51#123×C139—21no—
52C22⋊Q8×C139C2211yescharacteristic
53#121×C139—21no—
54#121×C139C2211yescharacteristic
55#120×C139—21no—
56C4×D4×C139C2211yescharacteristic
57C4×D4×C139C2211yescharacteristic
58C2×C22⋊C4×C139—21no—
59C2×Dic278C2311yescharacteristic
60C22×Dic139—21no—
61#14555775—41no—
62#14555773—22no—
63#14555773—41no—
64C2×C139⋊C8—41no—
65C2×C139⋊C8—41no—
66C2×C139⋊C8C2311yescharacteristic
67C2×C139⋊C8C2311yescharacteristic
68C2×C139⋊C8C2311yescharacteristic
69C2×C139⋊C8C2311yescharacteristic
70C4⋊Dic139—21no—
71C4⋊Dic139C2311yescharacteristic
72C4⋊Dic139C2311yescharacteristic
73C4⋊Dic139C2311yescharacteristic
74Dic139⋊C4—21no—
75Dic139⋊C4—21no—
76Dic139⋊C4—21no—
77Dic139⋊C4—21no—
78Dic139⋊C4—21no—
79C22⋊Dic139—21no—
80C22⋊Dic139—21no—
81C22⋊Dic139—21no—
82C4×Dic139—21no—
83C4×Dic139—21no—
84C24×C139—21no—
85#41×C139—22no—
86#41×C139—41no—
87C2×Q8×C139C2311yescharacteristic
88C2×D4×C139—22no—
89C2×D4×C139—21no—
90C2×D4×C139—21no—
91C2×D4×C139—21no—
92C2×D4×C139—41no—
93C2×D4×C139D411yescharacteristic
94C2×D4×C139C2311yescharacteristic
95C2×D4×C139C2311yescharacteristic
96C22×C4×C139—21no—
97C22×C4×C139—21no—
98C22×C4×C139C2311yescharacteristic
99C22×C4×C139C2311yescharacteristic
100C4⋊C4×C139—21no—
101C4⋊C4×C139D411yescharacteristic
102C4⋊C4×C139C2311yescharacteristic
103C22⋊C4×C139—21no—
104C22⋊C4×C139—21no—
105C22⋊C4×C139—21no—
106C22⋊C4×C139—21no—
107C22⋊C4×C139—21no—
108C22⋊C4×C139D411yescharacteristic
109C22⋊C4×C139D411yescharacteristic
110C42×C139C2311yescharacteristic
111Dic278—21no—
112Dic278—21no—
113C2×Dic139—21no—
114C2×Dic139—21no—
115C2×Dic139—21no—
116C2×Dic139—21no—
117C2×Dic139—42no—
118C139⋊C8—21no—
119C139⋊C8—21no—
120C139⋊C8—21no—
121C139⋊C8—21no—
122C23×C139—21no—
123C23×C139—21no—
124C23×C139—42no—
125C23×C139—42no—
126C23×C139—81no—
127C23×C139C2×D411yescharacteristic
128C23×C139C2×D411yescharacteristic
129Q8×C139—21no—
130Q8×C139—21no—
131D4×C139—22no—
132D4×C139—21no—
133D4×C139—21no—
134D4×C139—21no—
135D4×C139—42no—
136D4×C139—42no—
137D4×C139—81no—
138D4×C139#4112yes—
139C2×C4×C139—21no—
140C2×C4×C139—21no—
141C2×C4×C139—21no—
142C2×C4×C139—21no—
143C2×C4×C139—21no—
144C2×C4×C139—21no—
145C2×C4×C139—42no—
146C2×C4×C139—81no—
147C2×C4×C139C2×D411yescharacteristic
148C2×C4×C139C2×D411yescharacteristic
149C2×C4×C139C2×D411yescharacteristic
150C2×C4×C139C2×D411yescharacteristic
151C2×C4×C139C2411yescharacteristic
152C22×C139—21no—
153C22×C139—21no—
154C22×C139—21no—
155C22×C139—22no—
156C22×C139—21no—
157C22×C139—21no—
158C22×C139—41no—
159C22×C139—41no—
160C22×C139—41no—
161C22×C139—41no—
162C22×C139—41no—
163C22×C139—84no—
164C22×C139#13512yes—
165C22×C139C22×D411yescharacteristic
166C4×C139—21no—
167C4×C139—21no—
168C4×C139—21no—
169C4×C139—21no—
170C4×C139—41no—
171C4×C139—41no—
172C4×C139C2×#4111yescharacteristic
173C4×C139H(5,𝔽2)11yescharacteristic
174Dic139—41no—
175Dic139—41no—
176Dic139—41no—
177Dic139—41no—
178C2×C139—22no—
179C2×C139—41no—
180C2×C139—42no—
181C2×C139—81no—
182C2×C139#54611yescharacteristic
183C2×C139C2×#13511yescharacteristic
184C2×C139#57711yescharacteristic
185C139#329611yescharacteristic, complemented, Sylow
186#3296—1391nomaximal, Sylow
187#552—1391no—
188#546D13911yescharacteristic
189#488—1391no—
190#483—1391no—
191#482—1391no—
192#478—1391no—
193#467—1391no—
194#465—1391no—
195#464—1391no—
196#452—1391no—
197#450—1391no—
198C4×SD16—1391no—
199C8×D4—1391no—
200#416—1391no—
201C2×#102—1391no—
202C2×#41C2×D13911yescharacteristic
203C22×D4C2×D13911yescharacteristic
204C2×Q16—1391no—
205C2×SD16—1391no—
206C2×SD16—1391no—
207C22×C8—1391no—
208C22×C8—1391no—
209#126—2781no—
210#125—2781no—
211#125—1391no—
212#124C2×D13911yescharacteristic
213#123—21no—
214#123—2781no—
215C22⋊Q8—1391no—
216C22⋊Q8—1391no—
217C22⋊Q8C2×D13911yescharacteristic
218#121—21no—
219#121C2×D13911yescharacteristic
220#120—21no—
221C4×Q8—1391no—
222C4×D4C2×D13911yescharacteristic
223C4×D4C2×D13911yescharacteristic
224#117—2781no—
225#117—1391no—
226C2×C4⋊C4—1391no—
227C2×C22⋊C4—21no—
228#107—1391no—
229#106—1391no—
230#106—1391no—
231C4⋊C8—1391no—
232#103—1391no—
233#103—1391no—
234#103—1391no—
235#103—1391no—
236#102—1391no—
237#102—1391no—
238#102—1391no—
239#102—1391no—
240#102—1391no—
241#102—1391no—
242C22⋊C8—1391no—
243C22⋊C8—1391no—
244C4×C8—1391no—
245C24—21no—
246#41—22no—
247#41—41no—
248C2×Q8—1391no—
249C2×Q8C22×D13911yescharacteristic
250C2×D4—22no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—41no—
255C2×D4C22⋊D13911yescharacteristic
256C2×D4C22×D13911yescharacteristic
257C2×D4C22×D13911yescharacteristic
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—2781no—
261C22×C4C22×D13911yescharacteristic
262C22×C4C22×D13911yescharacteristic
263Q16—5561no—
264SD16—2782no—
265SD16—5561no—
266C2×C8—5561no—
267C2×C8—5561no—
268C2×C8—1391no—
269C2×C8—1391no—
270C2×C8—1391no—
271C2×C8—1391no—
272C4⋊C4—21no—
273C4⋊C4—2781no—
274C4⋊C4—2781no—
275C4⋊C4—2781no—
276C4⋊C4—2781no—
277C4⋊C4—2781no—
278C4⋊C4—2781no—
279C4⋊C4—1391no—
280C4⋊C4—1391no—
281C4⋊C4—1391no—
282C4⋊C4C22⋊D13911yescharacteristic
283C4⋊C4C22×D13911yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—2781no—
290C22⋊C4—2781no—
291C22⋊C4—2781no—
292C22⋊C4C22⋊D13911yescharacteristic
293C22⋊C4C22⋊D13911yescharacteristic
294C42—2781no—
295C42—2781no—
296C42C22×D13911yescharacteristic
297C23—21no—
298C23—21no—
299C23—42no—
300C23—42no—
301C23—81no—
302C23C2×C22⋊D13911yescharacteristic
303C23C2×C22⋊D13911yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—2781no—
307Q8—2781no—
308D4—22no—
309D4—21no—
310D4—21no—
311D4—21no—
312D4—42no—
313D4—42no—
314D4—81no—
315D4#1455578412yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—81no—
324C2×C4—2781no—
325C2×C4—2781no—
326C2×C4—2781no—
327C2×C4—2781no—
328C2×C4—5562no—
329C2×C4C2×C22⋊D13911yescharacteristic
330C2×C4C2×C22⋊D13911yescharacteristic
331C2×C4C2×C22⋊D13911yescharacteristic
332C2×C4C2×C22⋊D13911yescharacteristic
333C2×C4C23×D13911yescharacteristic
334C8—2781no—
335C8—2781no—
336C8—2781no—
337C8—2781no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—22no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—84no—
350C22#1798486212yes—
351C22C22×C22⋊D13911yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—5561no—
359C4—5561no—
360C4—5561no—
361C4—5561no—
362C4C2×#1455578411yescharacteristic
363C4#1798488711yescharacteristic
364C2—22no—
365C2—41no—
366C2—42no—
367C2—81no—
368C2#2258159711yescharacteristic
369C2C2×#1798486211yescharacteristic
370C2#2258176411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting, prime radical#546×C139C2
socleC22×C139C22×D4
hypercenter#546D139
hypocenterC139#3296
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #22581643C2semidirect
2. #22581307C2semidirect
3. #22581281C2semidirect
4. #22581274C2semidirect
5. #22581253C2semidirect
6. #22581192C2semidirect
7. #22581180C2semidirect
8. #22581172C2semidirect
9. #22581115C2semidirect
10. #22581104C2semidirect
11. C4×#14555773C2semidirect
12. D4×C139⋊C8C2semidirect
13. #22580949C2semidirect
14. C2×#17984763C2semidirect
16. C2×#14555775C22semidirect
20. C22×C139⋊C8C22semidirect
22. #17984834C22semidirect
26. #17984821C22semidirect
27. C4×Dic278C22semidirect
28. #17984801C22semidirect
31. #17984775C22semidirect
32. #17984773C22semidirect
33. #17984773C22semidirect
34. C4⋊(C139⋊C8)C22semidirect
35. #17984766C22semidirect
36. #17984766C22semidirect
37. #17984766C22semidirect
38. #17984765C22semidirect
46. C22⋊(C139⋊C8)C22semidirect
47. C4×C139⋊C8C22semidirect
185. C139#3296semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#225816432
#225813072
#225812812
#225812742
#225812532
#225811922
#225811802
#225811722
#225811152
#225811042
C4×#145557732
D4×C139⋊C82
#225809492
C2×#179847632
#546×C1392
#3296139